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Weather is notoriously difficult to predict. Models are subject to chaotic motion and must consider the initial conditions. The famous butterfly effect states that if a butterfly flaps its wings in Tahiti, that small event might cause a hurricane to hit Texas. This leads us to the following model: suppose that weather at time t is always between 0 and 1 and is governed by x_(t+1)=〖4x〗_t (1-x_t ). For x_0 = 0.2 and x_0 = 0.2000001, determine x_1; x_2;… x_50. Assume values for x closer to zero represent mild weather, and closer to 1 represent extreme weather. How do your calculations illustrate the butterfly effect? Support your answer with graphs.

Weather is notoriously difficult to predict. Models are subject to chaotic motion and must consider the initial conditions. The famous butterfly effect states that if a butterfly flaps its wings in Tahiti, that small event might cause a hurricane to hit Texas. This leads us to the following model: suppose that weather at time t is always between 0 and 1 and is governed by x_(t+1)=〖4x〗_t (1-x_t ). For x_0 = 0.2 and x_0 = 0.2000001, determine x_1; x_2;… x_50. Assume values for x closer to zero represent mild weather, and closer to 1 represent extreme weather. How do your calculations illustrate the butterfly effect? Support your answer with graphs.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Weather is notoriously difficult to predict. Models are subject to chaotic motion and must consider the initial conditions. The famous butterfly effect states that if a butterfly flaps its wings in Tahiti, that small event might cause a hurricane to hit Texas. This leads us to the following model: suppose that weather at time t is always between 0 and 1 and is governed by x_(t+1)=〖4x〗_t (1-x_t ). For x_0 = 0.2 and x_0 = 0.2000001, determine x_1; x_2;… x_50. Assume values for x closer to zero represent mild weather, and closer to 1 represent extreme weather. How do your calculations illustrate the butterfly effect? Support your answer with graphs. 

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